UdG researchers conclude that the public transport network in Barcelona is poorly connected

Using a method that applies the Mathematical Theory of Communication, University of Girona researchers Joan Saldaña and Josep Barberillo found that the interconnection between the subway, trains and trams in the Catalan capital is poor. This work has resulted in an article published in the scientific magazine Physica A.

The subway is the most widely used means of transport in big cities. Although its construction requires a high initial cost, the benefits are greater than the ones that the intercity bus, the car, the bike or the tram can offer. Fast, safe and clean, it reaches anywhere, it has a substantial capacity for travelers, the passage of vehicles is synchronized, and moving around is quite cheap. Moreover, the subway has a unique infrastructure that allows offering fixed timetables without being subject to traffic.

However, some aspects in the subway could be improved. Especially, in what refers to its navigation. When a traveler arrives to a big city and goes to a subway station, he first checks the information boards with a single purpose: to locate the stop that will drop him closer to his destination and to think of the best route to get there, taking into account the possibility of using other means of public transport such as suburban rail or bus.

Then, the questions start: what line or lines should I take and how do I transfer stations? To work the best route out is not always easy because of two common causes. The first one is the network size (large stations). The second one is about the network design, this is, the number of lines in a network, the interconnection between them, the central stations where many lines converge, etc.

Method
University of Girona (UdG) former student, Josep Barberillo –supervised by Professor Joan Saldaña (Department of Computer Science and Applied Mathematics)– has objectively quantified the difficulty of navigation in the large public transport network. To do so, they have applied concepts of the Mathematical Theory of Communication, a branch of mathematics and probability and statistics that aims to study the properties of the transmission process using a particular coding system between a source (transmitter) and a receiver through a communication channel. The article, entitled Navigation in large subway networks: An informational approach, was published in the prestigious journal Physica A.

The major public transport networks are composed of many stations that do not have a regular standard of connection between them. In a first step, it calculates what is called ‘information search’ between two stations, which means the probability of getting randomly from one station to another by the shortest route. If the search information is estimated on other stations, then it determines the accessibility to the network of that station. In a similar way, you can see the difficulty to get to a station from the so-called ‘location information’. Still, it is possible to get more relevant information.

With the average search information from all the stations, it is possible to compare different public transport networks such as Moscow, Barcelona, Paris and New York. It allows us to see how the number of stations and the design of the network affect the navigation. Also, UdG researchers have taken into account that networks just have two dimensions (they are flat). That’s why, for each network, they created a new 3D random one, without space restrictions. Thus, in the 3D version, the stations are connected between them allowing impossible links. The results indicate that the difficulty of navigation increases significantly as the size of the network also increases, and that aspects like geography have much to do.

Application
Finally, researchers have applied an indicator to estimate the difficulty of the journey between two stations according to the number of transfers that must be performed to go from one station to another. With the help of this indicator, when different companies are included in the same network, it can quantify the degree of the service integration and see whether they are well connected or not.

This method can be used in the design of lines new construction or in the expansion of an already existing network because it guarantees efficiency. It was implemented in the integrated network of Barcelona. The final conclusion is that the degree of interconnection between the companies that include the network is very low.